How to play Ferris Wheel
- Choose a target angle θ. The cabin starts at 3 o'clock and turns counter-clockwise.
- Find the quadrant and the reference angle, then decide the signs of cos θ and sin θ.
- Type both values, as decimals or as exact values such as √3/2. The dashed circle shows where you predict the cabin will stop.
- Press Play. Watch the shadows on the axes and the graph, and compare where the cabin stops with your prediction.
Sine and cosine are coordinates on a circle
On a circle of radius R centred at the origin, the point at angle θ is (R · cos θ, R · sin θ). On the unit circle, where R = 1, the coordinates are simply (cos θ, sin θ). This extends trigonometry beyond 90°: the signs depend on the quadrant, the values repeat every 360°, and the special angles have exact values: sin 30° = 1/2, sin 45° = √2/2, and sin 60° = √3/2.
A focused learning model
The wheel turns at a constant 1.5° per second, one turn every 4 minutes, so the cabin moves in uniform circular motion at v = R · ω ≈ 0.26 m/s, always tangent to the rim. The cabin's position is measured at its pivot on the rim, and its swinging is ignored. Playback runs 20 times faster than real time.